Finite Group Databasebeta

← #13080743

Subgroups — #13080743

Order 1408.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623365C211yesmaximal, characteristic
2#10623044C211yesmaximal, characteristic, complemented
3C11×#417C211yesmaximal, characteristic, complemented
4#10622852C211yesmaximal, characteristic, complemented
5#10622747C211yesmaximal, characteristic, complemented
6#10622740C211yesmaximal, characteristic, complemented
7#10622581C211yesmaximal, characteristic, complemented
8#10622423C211yesmaximal, characteristic, complemented
9#10622417C211yesmaximal, characteristic, complemented
10#10622409C211yesmaximal, characteristic, complemented
11#10622402C211yesmaximal, characteristic, complemented
12#10622397C211yesmaximal, characteristic, complemented
13#10622391C211yesmaximal, characteristic, complemented
14#10622377C211yesmaximal, characteristic, complemented
15#10622375C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×C11×M16C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20Q8×Dic11C2211yescharacteristic
21C2×#4326C2211yescharacteristic
22#66993—21no—
23#66993C2211yescharacteristic
24#66991—21no—
25#66991C2211yescharacteristic
26C2×#4324C2211yescharacteristic
27#66983—21no—
28#66983C2211yescharacteristic
29#66982—21no—
30C4×C22⋊D11—21no—
31C4×C22⋊D11C2211yescharacteristic
32#66979—21no—
33#66977C2211yescharacteristic
34C2×#4314C2211yescharacteristic
35C2×C8×D11C2211yescharacteristic
36#66951—21no—
37#66950C2211yescharacteristic
38#66945C2211yescharacteristic
39#66943C2211yescharacteristic
40#66942—21no—
41#66940C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49#66885C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66882C2211yescharacteristic
52#66880C2211yescharacteristic
53#66879C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
58#66872C2211yescharacteristic
59C11×#41—22no—
60C11×#41—41no—
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11—21no—
63C2×D4×C11C2311yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C2×C22⋊D11D411yescharacteristic
72#4343—22no—
73#4343—41no—
74C2×D44—21no—
75C2×D44C2311yescharacteristic
76C2×C4×D11—21no—
77C2×C4×D11C2311yescharacteristic
78C2×Dic22C2311yescharacteristic
79C11×M16—41no—
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4—21no—
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C22⋊Dic11—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11D411yescharacteristic
88#4326—22no—
89#4324—41no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4D411yescharacteristic
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4D411yescharacteristic
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109#4314—41no—
110C8×D11—41no—
111#3317—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11C2×D411yescharacteristic
114C22×D11—21no—
115C22×D11C2×D411yescharacteristic
116Q8×C11—21no—
117Q8×C11#4112yes—
118D4×C11—21no—
119D4×C11—21no—
120D4×C11—42no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2411yescharacteristic
130C22⋊D11—41no—
131C22⋊D11—42no—
132C22⋊D11—81no—
133C22⋊D11—81no—
134C22⋊D11—81no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140C2×Dic11C2×D411yescharacteristic
141D44—21no—
142D44—21no—
143D44—42no—
144C4×D11—21no—
145C4×D11—21no—
146C4×D11—42no—
147Dic22—21no—
148Dic22—21no—
149C8×C11—21no—
150C8×C11—21no—
151C11⋊C8—21no—
152C11⋊C8—21no—
153#552—111no—
154#550—111no—
155#490—111no—
156#482—111no—
157#481—111no—
158#479—111no—
159#468—111no—
160#465—111no—
161#460—111no—
162#452—111no—
163#452—111no—
164#441—111no—
165#435—111no—
166#417D1111yescharacteristic, complemented
167#416—111no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11C22×D411yescharacteristic
175C2×D11—21no—
176C2×D11—21no—
177C2×D11—21no—
178C2×D11—41no—
179C2×D11—41no—
180C2×D11—41no—
181C4×C11—21no—
182C4×C11—22no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11C2×#4111yescharacteristic
186C4×C11H(5,𝔽2)11yescharacteristic
187Dic11—21no—
188Dic11—21no—
189Dic11—21no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193C2×#41—111no—
194C2×#41C2×D1111yescharacteristic
195C2×Q16—111no—
196C2×SD16—111no—
197C2×SD16—111no—
198C2×M16C2×D1111yescharacteristic
199C22×C8—111no—
200#127—111no—
201#127—221no—
202#126—221no—
203#125—111no—
204#125—221no—
205#123—221no—
206C22⋊Q8—111no—
207C22⋊Q8—111no—
208#121—111no—
209#121—111no—
210#121—221no—
211#121—221no—
212C4×Q8—111no—
213C4×Q8—111no—
214C4×D4—111no—
215C4×D4—221no—
216#117—111no—
217#117—221no—
218C2×C4⋊C4C2×D1111yescharacteristic
219#107—111no—
220#106—111no—
221#106—111no—
222C4⋊C8—111no—
223#103—111no—
224#103—111no—
225#103C2×D1111yescharacteristic
226#103C2×D1111yescharacteristic
227#102—111no—
228#102—111no—
229#102—111no—
230#102—111no—
231#102C2×D1111yescharacteristic
232#102C2×D1111yescharacteristic
233C22⋊C8—111no—
234C22⋊C8—111no—
235#97—111no—
236C2×C11—41no—
237C2×C11—81no—
238C2×C11#54611yescharacteristic
239C2×C11#57511yescharacteristic
240C2×C11#57711yescharacteristic
241D11—41no—
242D11—81no—
243#41—22no—
244#41—41no—
245#41—222no—
246#41—441no—
247C2×Q8—111no—
248C2×Q8C22×D1111yescharacteristic
249C2×D4—21no—
250C2×D4—111no—
251C2×D4—111no—
252C2×D4—221no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4C22×D1111yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—111no—
261C22×C4—221no—
262C22×C4C22×D1111yescharacteristic
263Q16—222no—
264SD16—441no—
265SD16—441no—
266M16—41no—
267C2×C8—111no—
268C2×C8—111no—
269C2×C8—441no—
270C2×C8C22×D1111yescharacteristic
271C2×C8C22×D1111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—111no—
274C4⋊C4—111no—
275C4⋊C4—111no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4C22×D1111yescharacteristic
283C4⋊C4C22×D1111yescharacteristic
284C22⋊C4—111no—
285C22⋊C4—111no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C42—111no—
292C42—221no—
293C42—221no—
294C42—221no—
295C11#331711yescharacteristic, complemented, Sylow
296C23—21no—
297C23—111no—
298C23—221no—
299C23D4×D1111yescharacteristic
300Q8—21no—
301Q8—221no—
302Q8—221no—
303Q8#433912yes—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—221no—
308D4—221no—
309D4—442no—
310D4—441no—
311D4—442no—
312D4—881no—
313D4—881no—
314D4—881no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—111no—
323C2×C4—111no—
324C2×C4—111no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—442no—
331C2×C4D4×D1111yescharacteristic
332C2×C4C23×D1111yescharacteristic
333C8—21no—
334C8—21no—
335C8—221no—
336C8—221no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—221no—
344C22—221no—
345C22—221no—
346C22—441no—
347C22—441no—
348C22—441no—
349C22C2×D4×D1111yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—221no—
355C4—221no—
356C4—221no—
357C4—441no—
358C4—441no—
359C4—441no—
360C4C2×#433911yescharacteristic
361C4#6703711yescharacteristic
362C2—41no—
363C2—81no—
364C2—441no—
365C2—881no—
366C2#1062302111yescharacteristic
367C2#1062330411yescharacteristic
368C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#417C2
socleC22×C11C22×D4
prime radical#10623365C2
hypercenter#417D11
hypocenterC11#3317
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10623044C2semidirect
3. C11×#417C2semidirect
4. #10622852C2semidirect
5. #10622747C2semidirect
6. #10622740C2semidirect
7. #10622581C2semidirect
8. #10622423C2semidirect
9. #10622417C2semidirect
10. #10622409C2semidirect
11. #10622402C2semidirect
12. #10622397C2semidirect
13. #10622391C2semidirect
14. #10622377C2semidirect
15. #10622375C2semidirect
166. #417D11semidirect
295. C11#3317semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#106233652
#106230442
C11×#4172
#106228522
#106227472
#106227402
#106225812
#106224232
#106224172
#106224092
#106224022
#106223972
#106223912
#106223772
#106223752
#331711